On the Error Probability of Short Concatenated Polar and Cyclic Codes with Interleaving

In this paper, we study of the performance of the concatenation of a short polar code with an outer binary linear block code from a distance spectrum viewpoint. Our analysis targets the case where an outer cyclic code is employed together with an inner systematic polar code. A concatenated code ensemble is defined placing an interleaver at the input of the polar encoder. The introduced ensemble allows deriving bounds on the achievable error rates under maximum likelihood decoding, by applying the union bound to the (expurgated) average weight enumerators. The analysis suggests the need of careful optimization of the outer code, to attain low error floors. We also investigate the performance of a number of randomly chosen interleavers, with the aim to discuss the dispersion around the ensemble